Load-slip Response Research Articles

Cyclic response of laminated bamboo lumber nailed connection: Theoretical modelling and experimental investigations

The interest in the use of laminated bamboo lumber (LBL) as a new green building material is growing rapidly, but little work has been conducted on the cyclic response of LBL nailed connection, which consists of LBL middle member sandwiched between two LBL plates. Experiments on 90 LBL-to-LBL nailed connections are done to study the effect of nail diameter and loading direction to the grain on cyclic behavior of the connections. It is found that the failure mode of the connections loaded monotonically is due to the formation of two hinges of nail, which is quite different from the connections loaded cyclically. Two plastic hinges are also observed in nails during the cyclic tests, in addition, most of the nails in connections fail in low cycle fatigue fracture due to reversed bending of nails. The load-carrying capacity, stiffness, and energy-dissipating capacity of the connections can be significantly improved by using larger-diameter nails as connectors, while decreases slightly with the increase of loading direction to grain. Regarding to the displacement ductility ratio, whether monotonic loading or cyclic loading, the connections show low ductility performance. The equivalent viscous damping coefficient decreases with the increase of the nail diameter, and not relates with the loading direction to the grain. The load-slip response of the LBL nailed joints exhibits pinched hysteretic behavior with strength and stiffness degradation under cyclic loading. The modified Dolan theoretical model can be used to predict the cyclic response of the LBL nailed connections.

Analytical Model for Bond Behavior Prediction of CFRP-Concrete Joints with End Anchorage.

Use of the end anchorages can significantly control the debonding of CFRP-to-concrete bond interface, and improve the bearing capacity of CFRP strengthened concrete member. An analytical model was presented in this paper to predict the bond behavior and debonding process of CFRP-concrete bonded joint with end anchorage. The calculation formulas of bond failure load and effective bond length for anchored CFRP-concrete joint are derived from the proposed analytical model. According to these models and formulas, the influence of different bond lengths on the mechanical behaviors during the debonding process was analyzed. Results show the load-slip curves of end anchored CFRP-concrete joints could be divided into three branches: elastic stage, stable stage, and enhancement stage. As the bond length increases, the plateau length in stable stage increases. Besides, the bond failure load decreased firstly to a lower limit and then increased with the increase of bond length. The effective bond length of CFRP-concrete joint with end anchorage was longer than that of the external bonded joint, and the value of effective bond length for end anchored joint shall be at least 7.2/AB, where the parameters A and B were related to the interfacial properties of bonded joint. Furthermore, a single shear test was carried out on the end anchored CFRP-concrete bonded joint with different bond lengths, to verify the consistency of the proposed model and formulas. The analytical result of load-slip response at the load end, as well as the strain distribution of CFRP material and the bond failure load, was compared with the experimental result. The comparisons showed that the analytical results had a good agreement with the experimental results.

Analytical modelling of cold-formed steel-to-timber connections with inclined screws

An analytical model that can describe the load-slip response of cold-formed steel-to-timber connections, based on three components: timber embedment, screw bending and the axial pull-through, is presented. The model takes into consideration the screw inclination and the damage to the timber caused during the screw drilling process. The model was validated against available push-out test results, where it was shown that the model can accurately describe the ultimate load, the slip at ultimate load, and the two slip moduli, ks and ks,m, with mean model-to-test ratios of 1.01, 1.03, 1.09 and 0.96, respectively. The observed failure modes were also accurately predicted. Comparisons between the test data and the predictions of the EN 1995-1-1 design expressions showed that the Eurocode underestimated the ultimate loads by around 50% on average and overestimated the slip moduli by around 500% on average; the proposed model therefore offers a significant improvement over current design provisions.

Bond strength of reinforcing bars in ultra-high performance concrete: Experimental study and fiber–matrix discrete model

The study provided an experimental and theoretical investigation on the bond behavior of reinforcing bars in ultra-high performance concrete (UHPC) via a series of pullout tests. Test parameters included depth of concrete cover, bar embedment length and bar diameter. Failure mode, crack pattern and load-slip response were recorded and discussed under different test parameters. Test results indicated that inadequate concrete cover depth led to splitting failure while short embedment length resulted in concrete cone failure, corresponding to lower bond strengths. The bond strength increased up to 229.8% and the pullout energy increased 401.4% as the concrete cover depth increased from 0.5d to 2d. The development lengths were recommended to be 6d and 8d corresponding to the concrete cover depth of 2d, 1.5d, respectively. A theoretical bond strength model using fiber–matrix discrete concept was proposed and validated by comparing the calculated values with the test results and 343 test data collected from literature. The average ratios of the calculated results to the test results and collected data were 0.996 and 1.039, with a standard deviation of 0.255 and 0.252. The proposed model established the connection between the meso-scale bond property of fibers and matrix and the macro-scale bond strength of steel bars and UHPC, offering an alternative perspective in understanding the bond performance of steel bars in UHPC.

Experimental and numerical investigations of aluminium-timber composite beams with bolted connections

This paper presents an investigation of aluminium-timber composite (ATC) beams subjected to bending. In the proposed ATC beam, a timber slab was connected to an aluminium beam using bolts. ATC beams are a relatively new civil engineering solution and they are still being developed. The authors conducted push-out tests of the bolted connections and bending tests of the ATC beams. The slip moduli k0.4 and k0.6, and the load-carrying capacity of the connection were determined experimentally. Furthermore, the short-term behaviour, load carrying-capacity, mode of failure, load-deflection and load-slip response of the ATC beams with bolted connections were investigated. What is more, the authors used a calculation procedure for steel-concrete composite elements to calculate the load-carrying capacity of the ATC beams. The results from the analytical estimations were compared with the results from the laboratory tests. In addition, two non-linear finite element models of the tested composite beam were developed and verified against the experimental results. In the three-dimensional finite element model, laminated veneer lumber was described as an elastic-perfectly plastic material, and, as a consequence, this model did not need many input parameters. In the two-dimensional finite element model, laminated veneer lumber was described as an orthotropic material and its failure was captured using the Hashin damage model. It was an advanced model which needed many input parameters. The numerical results were similar to the experimental results.

Experimental study of deconstructable bolt shear connectors subjected to cyclic loading

An experimental study of deconstructable steel-concrete shear connectors using bolts under a low-cycle high-amplitude loading protocol is undertaken to investigate the effect of the concrete compressive strength, bolt size and its grade and size of clearance between the precast concrete slab and bolt on the load-slip response. To characterise the cyclic performance of the shear connectors, the ductility, strength degradation and absorbed energy are evaluated for all specimens. The experimental campaign includes twelve deconstructable shear connector specimens which were constructed and tested to failure. The failure modes involved severe concrete crushing, fracture of the bolt connectors, bolt bending and fracture, and bolt bending. In addition, three separate specimens were constructed and tested under monotonic loading and the results were compared with their cyclic test counterparts. The results obtained from the experiments show that the ultimate shear load capacity of the deconstructable steel-concrete shear connectors under cyclic loading was considerably less than that under monotonic loading. A structural model comprising of two parallel springs is also described and fitted to the experimental results to represent the load-slip response of the examined shear connectors.

Experimental behaviour and numerical modelling of timber-timber composite (TTC) joints

Push-out tests were conducted on 15 groups of symmetric timber-timber composite (TTC) joints with coach screw shear connectors. The push-out test results were used to characterise load-slip, peak load carrying capacity and failure mode of the composite shear connection between timber slab made of cross laminated timber (CLT) and timber beams/joists made of laminated veneer lumber (LVL) and/or glued laminated timber (GLT). Effect of coach screw size, type of engineered wood product (i.e. LVL-to-CLT and/or GLT-to-CLT), GLT grade, thickness of the CLT slab and orientation of load with respect to the outermost layer of CLT on the structural behaviour of the TTC joints were studied. In addition to the TTC connection tests, embedment strength of the LVL, CLT and GLT and bending yield strength of the screws were experimentally determined and the results were incorporated into a versatile nonlinear beam on inelastic foundation finite element (FE) model to capture the full range load-slip response of the TTC connection. The nonlinear FE models (including material and geometrical nonlinearities) were validated against the test data produced in this study and available in the literature and it was shown that the proposed nonlinear FE model can accurately predict the load-slip, stiffness and peak load carrying capacity of the TTC joints with screw shear connectors. The ultimate strength of the TTC joints were also estimated by modified European yield model (EYM) and comparison of the experimental peak load with EYM and FE predictions demonstrated the significant influence of the rope effect on the full range load-slip response and ultimate load carrying capacity of the TTC joints with dowel shear connectors.

Finite Element Analysis on Shear Behavior of High-Strength Bolted Connectors under Inverse Push-Off Loading

High-strength bolted shear connectors (HSBSCs), which can be demounted easily and efficiently during deconstruction, are recommended to replace the conventional steel studs in steel–concrete composite beams (SCCBs) to meet the requirements of sustainable development. The existing investigations on the behavior of HSBSCs mainly focus on the positive moment area of composite beams, in which the concrete slab is in compress condition. In this paper, a three-dimensional finite element model (FEM) was developed to investigate the performance of HSBSCs subjected to inverse push-off loading. Material nonlinearities and the interactions among all components were included in the FEM. The accuracy and reliability of the proposed FEM were initially validated against the available push-off test results. Load-carrying capacity and load–slip response of the HSBSCs under inverse push-off loading were further studied by the verified FEM. A parametric study was carried out to determine the influence of the concrete strength, the diameter and tensile strength of bolt and the clearance between the concrete slab and the bolt as well as the bolt pretension on the shear performance of HSBSCs. Based on the extensive parametric analyses, design recommendations for estimating the shear load at the first slip and load-bearing resistance of HSBSCs were proposed and verified.

Flexural behaviour of Steel Timber Composite (STC) beams

Structural performance of a new type of lightweight steel-timber composite (STC) beam has been investigated by conducting four-point bending tests on 21 specimens. This paper presents key findings on its structural performance parameters such as failure modes, load-deflection response, load-slip response, load-strain response, and the ultimate bending capacity by grouping 21 specimens into 7 subgroups based on various geometric characteristics. In the proposed STC beams, glulam slabs were connected to the steel beams using high-strength bolts, and the effect of different thickness and width of glulam slabs on the structural behaviour of STC beams were carefully investigated. In addition, the effective bending stiffness, deflection, and bending capacity of the STC beams were theoretically calculated based on elastic theory and compared with experimental values. For all considered specimens, timber slabs and steel beams showed good composite action. Increasing the thickness and width of the timber slabs can effectively limit the lateral deformation of the specimens, improve the bending capacity of the specimens, and provides a secant stiffness to the STC beams. It was observed that for the whole cross section of STC beams, the plane section assumption is not applicable, but the strains on timber and steel seemed to satisfy the plane section assumption individually. r (Gamma) method has been observed to better reflect the deformation capacity of STC beams. Analytical equations were derived to predict the elastic bending capacity of STC beams, and comparison between theoretical and experimental values showed good agreement.

Analytical modelling of bond-slip failure between epoxy bonded FRP and concrete substrate

In this paper, a set of explicit theoretical derivations from a generalised bond-slip model for an epoxy bonded fibre reinforced polymer (FRP) sheet to concrete are presented. The derivations address the maximum bond resistance, load-slip response, effective bond length and stress–strain distributions along the FRP. The generalised bond-slip model was compared with the existing bond-slip models to obtain the optimal bond-slip parameter using bond resistance results of single and double lap shear tests results available in the literature. The theoretical predictions using the optimal bond-slip parameters showed good agreement with experimental results of double lap shear tests. Furthermore, in order to understand the influence of the bond-slip parameters, a series of parametric studies are presented. Overall, the proposed bond-slip model and explicit derivations provide complete understanding of bonded FRP on concrete, as opposed to the partial understanding provided by empirical and semi-empirical models available in the literature.

Experimental and numerical study of shear connection in composite beams of steel and steel-fibre reinforced concrete

To explore the shear behaviour of high strength bolted connectors in steel-SFRC composite beams, push-out tests were carried out on 18 steel-fibre reinforced concrete (SFRC) specimens and 4 normal concrete (NC) specimens. The failure modes, ultimate shear strength, load-slip response as well as the shear stiffness of the tested specimens were determined accordingly. During the experiment, two failure modes that involved bolt shear failure and concrete splitting failure were observed in both NC and SFRC specimens. As the bolt-to-hole clearances of specimens were infilled, the slip plateau at the early loading stage therefor were avoided and the corresponding shear stiffness of bolted connectors increased as well. Compared to NC specimens, the extension of cracks on SFRC slabs were limited and the width of cracks efficiently decreased because of the addition of steel fibre in concrete. The ultimate shear strength of the bolted connectors in steel-SFRC composite beams was about 21.2% higher than that of the bolted connectors in steel-NC composite beams, with the volume percentage of steel fibre in concrete being approximate 1.0%. The applied pretension on bolted connectors had a significant effect on the shear stiffness of bolted connectors, but almost had no effect on the ultimate shear strength. The ultimate shear strength of bolted connectors increased with the increase of concrete compressive strength, bolt shank area and bolt tensile strength. Finite element models, which confirmed by the tested results, were also employed to perform the parametrical analysis involved in concrete compressive strength, as well as bolt pretension, and diameter and tensile strength. Upon the experimental and independent FE results, practical calculation formulas were further proposed, which can properly estimate the ultimate shear strength as well as the load-slip curves of high strength bolted connectors in steel-SFRC composite beams.

Experimental and numerical investigation of debonding process of the FRP plate-concrete interface

Single shear tests performed to study the debonding between the concrete and the FRP plate of 2 mm thickness are presented. Specimens with five different bond lengths have been tested. In order to investigate the debonding mechanism and measure the complete strain distribution, digital image correlation (DIC) method was applied. The shear stress and slip distribution curves were calculated from the strain distribution functions fitted from measured strain data. Based on the features of the shear stress transfer zone under different load levels, the whole loading process has been divided into four stages: (1) elastic stage; (2) cracking stage; (3) debonding stage; (4) failure stage. According to the relationship between the relative bearing capacity and bond length, a concept of efficient bond length was suggested. A bi-linear bond stress-slip model was calibrated by the constitutive parameters of the experimental shear stress-slip curves. Based on the bi-linear bond stress-slip relationship, a numerical model of FRP plate-concrete interface was built using the bonded-particle model (BPM) and the debonding process was numerically analyzed. The numerical results present good agreement with the experimental results in the load-slip response and the shear stress distribution along the bond length. The comparison between the experimental and the numerical results shows that BPM can effectively simulate the debonding process of the FRP plate-concrete interface.

Theoretical, experimental and numerical study of aluminium-timber composite beams with screwed connections

The present study investigated the structural behaviour of aluminium-timber composite (ATC) beams. In the proposed ATC system, a timber slab was connected to aluminium girders by hexagon head wood screws. ATC beams are a relatively new civil engineering solution and their behaviour should be investigated to develop relevant methods for calculating their resistance. The authors examined the stiffness and the strength of the screwed connection used to join an aluminium girder with a timber slab. The slip moduli k0.4 and k0.6, and the peak load capacity per one connector were determined experimentally in two push-out tests. These parameters are necessary for designing ATC beams, because the behaviour of an ATC system is depended on the stiffness and the strength of its connections. Moreover, two bending tests were conducted on ATC beams to investigate their short-term behaviour, determine their bending resistance and capture the mode of failure, load-deflection and load-slip response. Based on the guidelines for timber and composite (steel-timber and steel-concrete) elements, the authors of this paper proposed the methods for calculating the bending resistance of the ATC beams, and the stiffness and strength of their screwed connections. The results obtained in the experimental tests were compared with the results from the analytical estimations. In addition, non-linear 3D finite element (FE) models of the tested composite beams and connections were developed and verified against the experimental results. The comparison between the experimental and numerical results demonstrated that the adopted 3D models were able to adequately capture the response of the ATC composite beams and their connections. These models may be used in further numerical analysis of ATC structures, e.g., to evaluate the impact of the number of the shear connectors on the load-bearing capacity of an ATC beam.

Behavior and strength of headed stud shear connectors in ultra-high performance concrete of composite bridges

This study presents an experimental and numerical investigation on the static behavior of headed stud shear connectors in ultra-high performance concrete (UHPC) of composite bridges. Four push-out specimens were tested. It was found that no cracking, crushing or splitting was observed on the concrete slab, indicating that UHPC slab exhibited good performance and could resist the high force transferred from the headed studs. The numerical and experimental results indicated that the shear capacity is supposed to be composed of two parts stud shank shear contribution and concrete wedge block shear contribution. The stiffness increment of a stud in UHPC was at least 60% higher than that in normal strength concrete. Even if the stud height was reduced from 6d to 2d, there was no reduction in the shear strength of a stud. Short stud shear connectors with an aspect ratio as small as 2 could develop full strength in UHPC slabs. An empirical load-slip equation taking into account stud diameter was proposed to predict the load-slip response of a stud. The reliability and accuracy of the proposed load-slip equation was verified by the experimental and numerical load-slip curves.

Experimental study of the short-term and long-term behavior of perfobond connectors

Recently, perfobond connectors for steel-concrete composite structures have received extensive research attention due to their excellent bonding and fatigue performance, and the construction convenience. However, the research on the long-term behavior of perfobond connectors was seldom reported. This paper presents the results of laboratory tests on perfobond connectors, including twenty short-term specimens and six long-term specimens. Parametric study was conducted to investigate the influence of the hole diameter in the connector, the number of the holes, the thickness of the connector, the concrete strength as well as the diameter of the transverse rebar on the shear performance of perfobond connectors. For the short-term test series, the failure modes of the connector, the load-slip response, the ultimate shear bearing capacity and the load-strain curves of transverse rebar were studied. For the long-term test series, the transverse rebar strain, the relative slip between the steel beam and the concrete slab and the stress around the holes with duration of loading were discussed. The shear performance of perfobond connectors after long-term loading was also investigated. Finally, based on the test data from both this paper and open literature, a model was proposed to predict the shear bearing capacity of perfobond connectors.

Numerical modeling of FRP strips bonded to a masonry substrate

In this paper, the debonding phenomenon in FRP-strengthened masonry is numerically investigated. A 3D finite element model is developed to reproduce an experimental set-up of single-lap shear tests. Brick and mortar are modeled separately by two plastic-damage constitutive laws. Perfect adhesion between the FRP strip and masonry is assumed. Firstly, the numerical model is used to simulate experimental tests. A good agreement between the experimental and numerical results in terms of load-slip response is observed. Then, further finite element analyses are carried out to gain an insight on the effects of (i) the thickness and mechanical properties of the mortar joints and (ii) the width of the FRP strip on the debonding phenomenon.

CFRP-to-steel bonded joints subjected to cyclic loading: An experimental study

Pseudo-cyclic and cyclic loading were applied to CFRP-to-steel bonded joints built with two different CFRP laminates. In this paper, the strength capacity and bond-slip curves are presented and compared. The modes of failure are also described and associated with the types of material used, and the observed performances are correlated. The analysis of the results showed a threshold value for loading and amplitude level, below which the cyclic loading caused no detectable damage. For cycles above that limit, the region of the joints around the loaded end presented degradation reflected on the bond-slip stiffness and on the increase of residual deformation. It was found that the normalized dissipated energies either obtained from the bond-slip relationship or from the load-slip response had the same trend. The experimental data allowed also to establish a relationship between the damage developed within the interface and the normalized slip. A preliminary estimate of fatigue limit based on those data is suggested.

Finite element modelling of composite cold-formed steel flooring systems

The findings from a numerical investigation into the degree of composite action that may be mobilised within floor systems comprising cold-formed steel joists and wood-based particle boards are presented herein. Finite element models have been developed, simulating all the components of the examined systems, as well as the interaction between them. The models include initial geometric imperfections, the load-slip response of the fasteners employed to achieve the shear connection as well as both geometric and material nonlinearities. The developed models were first validated against 12 physical tests reported in the literature, which showed them to be capable of accurately capturing the load-deformation curves and failure modes exhibited by the tested specimens. Parametric studies were then performed to examine the influence of key parameters on the structural behaviour of these systems, including the depth and thickness of the cold-formed steel section, as well as the spacing of the employed fasteners; in total, about 100 systems have been examined. Significant benefits in terms of structural response have been identified from the presented numerical study as a result of the mobilisation of composite action; for the systems investigated, which were of typical, practical proportions, up to 140% increases in moment capacity and 40% increases in stiffness were found. The presented research reveals the substantial gains in structural performance and the influence of the key governing parameters for this novel form of composite construction.

Modelling FRP-to-substrate joints using the bilinear bond-slip rule with allowance for friction—Full-range analytical solutions for long and short bonded lengths

Methods for simulating the mechanics of debonding and predicting global load-slip (P-Δ) response from local bond stress versus slip (τ-δ) relationships can vary significantly in their complexity. It is generally accepted that an adequate representation of intermediate crack debonding can be achieved by considering only mode-II (shear) fracture along the interfacial bond, a problem that can be solved by accounting for one-dimensional fields of elastic stress and strain in the substrate and plate, and nonlinear interfacial slip and shear stress along the bond. In this paper, full-slip-range analytical solutions are presented for the bilinear τ-δ rule with allowance for residual friction. The procedure is capable of modelling the entire debonding process over both long and short bonded lengths. This is an extension of previous works which are either inapplicable to all bonded lengths or do not allow for residual strength. Applicability of the formulation can range from externally-bonded or near-surface-mounted FRP plates, to embedded bars or bolts in brittle substrates such as concrete, rock or masonry. The versatility and low computational effort required to apply the developed formulation makes it ideal for both directly predicting the P-Δ relationship from known τ-δ parameters, or conversely for extracting a τ-δ relationship from a reference P-Δ curve using inverse calibration. While it is not the purpose of this paper to propose a bond model for any specific type of system, a framework is proposed for doing so. Significantly this framework addresses the difficulty in identifying a unique solution of local properties from experimental data, and highlights that the bonded length has an important influence on the reliability of extracted results.

Composite connections between CLT slab and steel beam: Experiments and empirical models

A composite floor comprising of steel beams connected to cross laminated timber (CLT) panels is a sustainable alternative to composite floors with reinforced concrete slab. The structural performance of the steel-CLT floor depends strongly on the load-slip behaviour (particularly the stiffness and strength) of the shear connection between the steel beams and the CLT slabs. In this paper, the short-term behaviour of steel-CLT joints is studied by laboratory push-out experiments conducted on CLT-steel-CLT specimens, being analogous to familiar push tests on steel-concrete specimens. In addition to coach screws and bolts, a high-performance steel-CLT composite connection comprising of high-strength bolted shear connectors embedded in pockets of grout is proposed and tested. The push-out experiments are used to determine the load-slip, failure mode, stiffness and ultimate strength/capacity of the steel-CLT composite joints and to calibrate an empirical formula for the load-slip response of the CLT-to-steel connections. Furthermore, simple empirical formulae for the stiffness and ultimate capacity of the CLT-to-steel composite connections are proposed.